## Abstract

The paper considers a game-theoretic model of a dynamic optimal-purpose problem using the example of the labor market functioning. A deterministic model of the workers optimal distribution among enterprises is described taking into account changing conditions over a period of time. At each moment of time, the state of the employee and the enterprise are determined. Moments of time are moments of the system stationary states. In each stationary state, a game in normal form is determined. In the game there is a compromise situation, optimal policy, and the system's income from appointments is calculated as the sum of the payoff functions of all players. The functioning of the labor market as a system for some periods of time is presented as a multi-step game on a tree. In a one-step game based on the principle of compromise set optimality, there is a compromise situation and the corresponding compromise control vector. On the multi-step game tree, there is a compromise income of the system in a few steps, when a sequence of games was realized, and a compromise path corresponding to a sequence of compromise control vectors. The compromise system income and the sequence of compromise controls are found using dynamic programming recurrence relationships. Thus, it is possible to indicate the optimal behavior of all participants in the labor market at any given time.

Original language | English |
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Title of host publication | Proceedings - 2019 1st International Conference on Control Systems, Mathematical Modelling, Automation and Energy Efficiency, SUMMA 2019 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 229-234 |

Number of pages | 6 |

ISBN (Electronic) | 9781728149110 |

DOIs | |

State | Published - Nov 2019 |

Event | 1st International Conference on Control Systems, Mathematical Modelling, Automation and Energy Efficiency, SUMMA 2019 - Lipetsk, Russian Federation Duration: 20 Nov 2019 → 22 Nov 2019 |

### Publication series

Name | Proceedings - 2019 1st International Conference on Control Systems, Mathematical Modelling, Automation and Energy Efficiency, SUMMA 2019 |
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### Conference

Conference | 1st International Conference on Control Systems, Mathematical Modelling, Automation and Energy Efficiency, SUMMA 2019 |
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Country/Territory | Russian Federation |

City | Lipetsk |

Period | 20/11/19 → 22/11/19 |

## Scopus subject areas

- Organizational Behavior and Human Resource Management
- Mechanical Engineering
- Control and Optimization
- Modelling and Simulation
- Control and Systems Engineering

## Keywords

- dynamic problem
- game theory
- labor resources
- optimal assignment